Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

The potential difference across a resistor 'r' carrying current 'I' IS Ir.
( 1 ) If the potential difference across 'r' is measured using a voltmeter of resistence 'Rv', s
how that the reading of voltmeter is less thsn the true value.
2. find the percentage error in measuring the potential differene by a voltmeter
3.At what value of Rv, does the voltmeter measures the true potential difference
Asked by Rajeev | 17 Feb, 2016, 10:55: AM
answered-by-expert Expert Answer
Consider the above circuit.
Since the voltmeter has a resistance of Rv, suppose that the current I1 passes through it. 
So, the current through resistor R is (I-I1).
Since the voltmeter is connected parallel to the resistor, the potential difference across the voltmeter is equal to the potential difference across the resistor R.
So applying ohm's law
I1Rv = (I-I1) R 
IR = I1(R + Rv)
begin mathsize 14px style straight I subscript 1 space equals space fraction numerator RI over denominator straight R plus straight R subscript straight v end fraction end style
Substituting the values of I1 in (I-I1), we get,
begin mathsize 14px style straight V equals open parentheses straight I minus fraction numerator RI over denominator straight R plus straight R subscript straight v end fraction close parentheses straight R end style
  begin mathsize 14px style equals open parentheses straight I minus fraction numerator RI over denominator straight R plus straight R subscript straight v end fraction close parentheses straight R equals RI minus fraction numerator straight R squared straight I over denominator straight R plus straight R subscript straight v end fraction end style
The reading of voltmeter is less bybegin mathsize 14px style fraction numerator straight R squared straight I over denominator straight R plus straight R subscript straight v end fraction end style.
Percentage error:

begin mathsize 14px style fraction numerator Actual space potential space difference minus Error over denominator Actual space potential space difference end fraction cross times 100 end style
begin mathsize 14px style fraction numerator RI minus begin display style fraction numerator straight R squared straight I over denominator straight R plus straight R subscript straight v end fraction end style over denominator RI end fraction cross times 100 fraction numerator RI left parenthesis straight R plus straight R subscript straight v right parenthesis minus straight R squared straight I over denominator straight R plus straight R subscript straight v end fraction cross times 1 over RI cross times 100 fraction numerator straight R squared straight I plus RR subscript straight v straight I minus straight R squared straight I over denominator RI left parenthesis straight R plus straight R subscript straight v right parenthesis end fraction cross times 100 fraction numerator RR subscript straight v straight I over denominator RI left parenthesis straight R plus straight R subscript straight v right parenthesis end fraction cross times 100 fraction numerator straight R subscript straight v over denominator straight R plus straight R subscript straight v end fraction cross times 100 end style
When begin mathsize 14px style straight R subscript straight v rightwards arrow infinity end style, the error in potential difference begin mathsize 14px style fraction numerator straight R squared straight I over denominator straight R plus straight R subscript straight v end fraction rightwards arrow 0 end style. So the voltmeter will measure true potential difference.
Answered by Faiza Lambe | 22 Feb, 2016, 02:50: PM
CBSE 12-science - Physics
Asked by sampathsanjaykalla | 01 May, 2020, 09:34: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by ransinghkanoh | 18 Mar, 2019, 11:04: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by pardeepkumar2281 | 04 Oct, 2018, 09:41: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by kv.cyfuture | 03 Sep, 2018, 12:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 28 Apr, 2015, 09:54: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 28 Apr, 2015, 09:58: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 28 Apr, 2015, 10:12: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×